Data normalization

Initialization

We start the analysis by initializing the packages required for all the analysis performed in this section. We also define the root directory, within which all the input/output operations for this project will be performed. At the end of this document, a detailed software version information is provided for easier reproducibility of the analysis.

Normalization methodology

We use two different normalization strategy to answer specific questions -

  • For a given plate \(i\), the Cytoplasmic and Mitochondrial roGFP2 ratios are normalized by the median of all controls in the same plate i.e for cytoplasm - \[NormCyto(i) = \frac{Cyto_i} {median(Ctrl_i)}\] and for mitochondria, \[NormMito(i) = \frac{Mito_i} {median(Ctrl_i)}\]

This type of control based plate normalization will be suitable in comparing the redox levels in across organells and nutrients since the roGFP2 ratios has been commonly normalized to the plate control.

  • For a given plate \(i\) with the Cytoplasmic and Mitochondrial roGFP2 ratios \(j\) are normalized by their respective plate specific median roGFP2 ratios i.e for cytoplasm - \[NormCyto_{i} = \frac{Cyto_{ij} - median(Cyto_{i})} {mad(Cyto_{i})}\] and for mitochondria, \[NormMito_{i} = \frac{Mito_{ij} - median(Mito_{i})} {mad(Mito_{i})}\]

This type of organelle specific normalization will be suitable in comparing the redox levels in each organelle across all plates. Since this type of normalization tells us how far are the values from the plate median.

Furthermore, for each normalization strategy, we also summarized the quadruplicated values per gene by taking the median of the scaled values. Due to our outlier removal strategy in the previous section, many NA values were introduced. Each mutant has 4 values, we removed mutants with 2 or more NA values and those with only one NA value was substituted with the median of the other 3 observed values. Next, there were also multiple copies of the same mutants (genes) in either the same plate or different plates. We summarized them by taking the set of quadruplicated or median summarized values which have the maximum absolute median value.

Eventually, we generate the following -

  • A table with all the replicate values per organelle and nutrient conditions and the the median summarized value from all plates
  • A matrix with gene/mutants in rows and all combinations of organelle, nutrient and replicates (and median summarized value) in the column

Below is the table of cleaned raw data that we will use in our analysis.

rawDatCleaned = readRDS(paste0(path, "data/workspaces/YeastRedox_MATa_RawData_ForZNorm.RDS"))
rawDatCleaned = rawDatCleaned[, c("Plate", "Well_96", "Well", "Group", "Content", 
    "SystematicName", "SGD.ID", "Gene.Symbol", "roGFP2.ratio", "Type")]

rawDatCleaned_ctrlfilt = readRDS(paste0(path, "data/workspaces/YeastRedox_MATa_RawData_ForCtrlNorm.RDS"))
rawDatCleaned_ctrlfilt = rawDatCleaned_ctrlfilt[, c("Plate", "Well_96", "Well", "Group", 
    "Content", "SystematicName", "SGD.ID", "Gene.Symbol", "roGFP2.ratio", "Type")]

normalizeScreenData = function(normMethod) {
    
    if (normMethod == "fracControl") {
        normDat = split(rawDatCleaned_ctrlfilt, as.character(rawDatCleaned_ctrlfilt$Type))
        normDat = lapply(normDat, function(x) {
            split(x, x$Plate)
        })
    }
    
    if (normMethod == "robustZ") {
        normDat = split(rawDatCleaned, rawDatCleaned$Type)
        normDat = lapply(normDat, function(x) {
            split(x, x$Plate)
        })
    }
    
    normDatReps = normDat
    
    for (i in 1:length(normDat)) {
        for (j in 1:length(normDat[[i]])) {
            tmp = droplevels(normDat[[i]][[j]])
            
            if (nrow(tmp) > 0) {
                
                #---------------------------------------------------------------------------------------------
                # Separate Controls, Cytoplasam and Mitochondrial roGFP2 ratios per plate
                #---------------------------------------------------------------------------------------------
                
                # Control
                tmp.ctrl = droplevels(tmp[tmp$Content == "Control", ])
                
                # Cytoplasm
                tmp.cyto = droplevels(tmp[tmp$Content == "Cytoplasm", ])
                
                # Mitochondria
                tmp.mito = droplevels(tmp[tmp$Content == "Mitochondria", ])
                
                rm(tmp)
                
                #---------------------------------------------------------------------------------------------
                # Compute the corresponding normalization factors (median & median absolute
                # deviation)
                #---------------------------------------------------------------------------------------------
                
                # Normalizing factor - Control
                nf.ctrl.med = median(tmp.ctrl$roGFP2.ratio, na.rm = T)
                
                # Normalizing factor - Cytoplasm
                nf.cyto.med = median(tmp.cyto$roGFP2.ratio, na.rm = T)
                nf.cyto.mad = mad(tmp.cyto$roGFP2.ratio, na.rm = T)
                
                # Normalizing factor - Mitochondria
                nf.mito.med = median(tmp.mito$roGFP2.ratio, na.rm = T)
                nf.mito.mad = mad(tmp.mito$roGFP2.ratio, na.rm = T)
                
                #---------------------------------------------------------------------------------------------
                # The two normalization strategies (plate control and median based)
                #---------------------------------------------------------------------------------------------
                
                # Normalization 1 - Plate control based
                if (normMethod == "fracControl") {
                  tmp.cyto$roGFP2.ratio = tmp.cyto$roGFP2.ratio/nf.ctrl.med
                  tmp.mito$roGFP2.ratio = tmp.mito$roGFP2.ratio/nf.ctrl.med
                }
                
                # Normalization 2 - Plate median based
                if (normMethod == "robustZ") {
                  tmp.cyto$roGFP2.ratio = (tmp.cyto$roGFP2.ratio - nf.cyto.med)/nf.cyto.mad
                  tmp.mito$roGFP2.ratio = (tmp.mito$roGFP2.ratio - nf.mito.med)/nf.mito.mad
                }
                
                rm(nf.ctrl.med, nf.cyto.med, nf.cyto.mad, nf.mito.med, nf.mito.mad)
                
                #---------------------------------------------------------------------------------------------
                # Normalized data with replicates - coverting from long to wide table format
                #---------------------------------------------------------------------------------------------
                
                #---Cytoplasm---#
                
                tmp.cyto.repl = tmp.cyto %>% select(Gene.Symbol, Plate, Group, roGFP2.ratio, 
                  Type, Content) %>% group_by(Gene.Symbol, Group) %>% mutate(pseurep = paste0("roGFP2_ratio_", 
                  1:n())) %>% spread(key = pseurep, value = roGFP2.ratio) %>% ungroup() %>% 
                  select(-Group) %>% rename(Genes = Gene.Symbol, Nutrient = Type, 
                  Organelle = Content)
                
                #---Mitochondria---#
                
                tmp.mito.repl = tmp.mito %>% select(Gene.Symbol, Plate, Group, roGFP2.ratio, 
                  Type, Content) %>% group_by(Gene.Symbol, Group) %>% mutate(pseurep = paste0("roGFP2_ratio_", 
                  1:n())) %>% spread(key = pseurep, value = roGFP2.ratio) %>% ungroup() %>% 
                  select(-Group) %>% rename(Genes = Gene.Symbol, Nutrient = Type, 
                  Organelle = Content)
                
                #--Compilation---#
                
                if (identical(ncol(tmp.cyto.repl), ncol(tmp.mito.repl))) {
                  normDatReps[[i]][[j]] = rbind(tmp.cyto.repl, tmp.mito.repl)
                } else {
                  normDatReps[[i]][[j]] = NA
                }
                
                # Deleting
                rm(tmp.ctrl, tmp.cyto, tmp.mito, tmp.cyto.repl, tmp.mito.repl)
            }
        }
        rm(j)
    }
    rm(i)
    
    res = lapply(normDatReps, function(x) {
        x = x[!is.na(x)]
        x = do.call("rbind", x)
        x = as.data.frame(x)
        x$Plate = factor(x$Plate)
        x$Organelle = factor(x$Organelle, levels = c("Mitochondria", "Cytoplasm"))
        x$Nutrient = factor(x$Nutrient, levels = c("Glucose", "Galactose", "Glycerol"))
        rownames(x) = 1:nrow(x)
        return(x)
    })
    
    res = do.call("rbind", res)
    
    #-------------------------------------------------------------------------------------------------
    # Summarizing mutiple mutants (i.e same gene) from the same or different plates
    # Also dropping genes with 2 or more NA values For genes with just 1 NA value,
    # replacing it with the median of the remaining 3 observed values
    #-------------------------------------------------------------------------------------------------
    
    res = res %>% rowwise() %>% mutate(Median_roGFP2_ratio = median(c(roGFP2_ratio_1, 
        roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4), na.rm = T), NA_per_row = sum(is.na(c(roGFP2_ratio_1, 
        roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4)))) %>% filter(NA_per_row < 
        2) %>% ungroup() %>% mutate_at(vars(starts_with("roGFO2_ratio_")), function(x) ifelse(is.na(x), 
        .$Median_roGFP2_ratio, x)) %>% select(-NA_per_row) %>% group_by(Organelle, 
        Nutrient, Genes) %>% top_n(n = 1, abs(Median_roGFP2_ratio)) %>% ungroup()
    
    #-------------------------------------------------------------------------------------------------
    # Compiling all replicates across organelles and nutrient conditions into a
    # single matrix
    #-------------------------------------------------------------------------------------------------
    
    redoxMat = data.table(res[, c("Genes", "Nutrient", "Organelle", "roGFP2_ratio_1", 
        "roGFP2_ratio_2", "roGFP2_ratio_3", "roGFP2_ratio_4")])
    redoxMat = dcast(redoxMat, Genes ~ Organelle + Nutrient, fun.aggregate = function(x) {
        x
    }, fill = NA, value.var = c("roGFP2_ratio_1", "roGFP2_ratio_2", "roGFP2_ratio_3", 
        "roGFP2_ratio_4"))
    
    redoxMat = redoxMat[, c(1, 2, 8, 14, 20, 3, 9, 15, 21, 4, 10, 16, 22, 5, 11, 
        17, 23, 6, 12, 18, 24, 7, 13, 19, 25)]
    
    redoxMat = data.frame(redoxMat, row.names = 1, stringsAsFactors = F)
    
    #-------------------------------------------------------------------------------------------------
    # Compiling the median values across organelles and nutrient conditions into a
    # single matrix
    #-------------------------------------------------------------------------------------------------
    
    redoxMat_median = data.table(res[, c("Genes", "Nutrient", "Organelle", "Median_roGFP2_ratio")])
    redoxMat_median = dcast(redoxMat_median, Genes ~ Organelle + Nutrient, fun.aggregate = function(x) {
        x
    }, fill = NA, value.var = "Median_roGFP2_ratio")
    
    redoxMat_median = data.frame(redoxMat_median, row.names = 1, stringsAsFactors = F)
    
    #-------------------------------------------------------------------------------------------------
    # Putting all the results into one
    #-------------------------------------------------------------------------------------------------
    
    res = list(redox_table = res, redox_replicates = redoxMat, redox_median = redoxMat_median)
    rm(normDat, normDatReps, redoxMat, redoxMat_median)
    return(res)
}

normDat.ctrNorm = normalizeScreenData(normMethod = "fracControl")
normDat.Znorm = normalizeScreenData(normMethod = "robustZ")

Normalized data overview

We normalize the data as described above, below is the summary and the distribution of the normalized data -

  • For per plate normalization based on plate specific control
    Genes               Plate            Nutrient           Organelle    
 Length:20194       104    :  536   Glucose  :6832   Mitochondria:10980  
 Class :character   102    :  530   Galactose:6813   Cytoplasm   : 9214  
 Mode  :character   107    :  524   Glycerol :6549                       
                    142    :  502                                        
                    116    :  476                                        
                    101    :  467                                        
                    (Other):17159                                        
 roGFP2_ratio_1   roGFP2_ratio_2   roGFP2_ratio_3   roGFP2_ratio_4  
 Min.   :0.0001   Min.   :0.0001   Min.   :0.0001   Min.   :0.0001  
 1st Qu.:1.2289   1st Qu.:1.2253   1st Qu.:1.2178   1st Qu.:1.2198  
 Median :1.5502   Median :1.5436   Median :1.5345   Median :1.5437  
 Mean   :1.5739   Mean   :1.5703   Mean   :1.5647   Mean   :1.5654  
 3rd Qu.:1.8616   3rd Qu.:1.8586   3rd Qu.:1.8481   3rd Qu.:1.8485  
 Max.   :5.0074   Max.   :5.7204   Max.   :4.6066   Max.   :5.0642  
                                                    NA's   :1285    
 Median_roGFP2_ratio
 Min.   :0.0001     
 1st Qu.:1.2243     
 Median :1.5486     
 Mean   :1.5690     
 3rd Qu.:1.8518     
 Max.   :4.5752
  • For per plate normalization based on median organelle specific values
    Genes               Plate            Nutrient           Organelle    
 Length:20767       104    :  546   Glucose  :7057   Mitochondria:11261  
 Class :character   102    :  532   Galactose:6967   Cytoplasm   : 9506  
 Mode  :character   107    :  524   Glycerol :6743                       
                    142    :  499                                        
                    116    :  483                                        
                    105    :  477                                        
                    (Other):17706                                        
 roGFP2_ratio_1       roGFP2_ratio_2      roGFP2_ratio_3      roGFP2_ratio_4   
 Min.   :-13.129041   Min.   :-14.12713   Min.   :-10.55667   Min.   :-8.8123  
 1st Qu.: -0.669767   1st Qu.: -0.68972   1st Qu.: -0.72973   1st Qu.:-0.7219  
 Median :  0.005724   Median : -0.00748   Median : -0.05430   Median :-0.0490  
 Mean   :  0.042939   Mean   :  0.02005   Mean   : -0.01189   Mean   :-0.0141  
 3rd Qu.:  0.674491   3rd Qu.:  0.67449   3rd Qu.:  0.63977   3rd Qu.: 0.6186  
 Max.   : 27.784782   Max.   : 27.77066   Max.   : 28.68175   Max.   :27.7560  
                                                              NA's   :1325     
 Median_roGFP2_ratio
 Min.   :-8.44525   
 1st Qu.:-0.58048   
 Median :-0.04568   
 Mean   : 0.01706   
 3rd Qu.: 0.54324   
 Max.   :27.77772
  • Number of mutants per condition
   GalactoseCytoplasm GalactoseMitochondria      GlucoseCytoplasm 
                 3074                  3739                  3300 
  GlucoseMitochondria     GlycerolCytoplasm  GlycerolMitochondria 
                 3532                  2840                  3709
  • Similarity between the normalization strategies
plotList = vector("list", 6)
names(plotList) = c("Glucose-Cytoplasm",   "Glucose-Mitochondria",
                    "Galactose-Cytoplasm", "Galactose-Mitochondria",
                    "Glycerol-Cytoplasm",  "Glycerol-Mitochondria")

plotListTop = plotList

for(i in c("Glucose", "Galactose", "Glycerol"))
{
  for(j in c("Cytoplasm", "Mitochondria"))
  {
    a = normDat.Znorm$redox_table[which(normDat.Znorm$redox_table$Nutrient == i & normDat.Znorm$redox_table$Organelle == j),]
    a = a[, c("Genes", "Median_roGFP2_ratio")]
    colnames(a) = c("Genes", "Znorm")
    
    b = normDat.ctrNorm$redox_table[which(normDat.ctrNorm$redox_table$Nutrient == i & normDat.ctrNorm$redox_table$Organelle == j),]
    b = b[, c("Genes", "Median_roGFP2_ratio")]
    colnames(b) = c("Genes", "Ctrlnorm")
    
    df = merge(a,b)
    
    topZ = quantile(df$Znorm, probs = c(0.05, 0.95))
    topC = quantile(df$Ctrlnorm, probs = c(0.05, 0.95))
    
    df_top = df[which(df$Znorm < topZ[1] | df$Znorm > topZ[2] | df$Ctrlnorm < topC[1] | df$Ctrlnorm > topC[2]),]
    
    id = paste(i,j,sep="-")
    
    plotList[[id]] = ggscatter(df, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman", label.x = -10, label.y = 3, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
     plotListTop[[id]] = ggscatter(df_top, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman",  label.x = -10, label.y = 3, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
    
    rm(a, b, df,df_top, topZ, topC, id)
  }
  rm(j)
}
rm(i)

Plotting the correlation between the two normalization techniques for all matching mutants

Plotting the correlation between the two normalization techniques using ONLY the top hits 5% (high/low) roGFP2 ratios from either normalization method

Sample similarity - Dimensionality reduction

Next, we apply the dimensionality reduction method Multidimesional scaling (MDS) on the roGFP2 ratio values normalized by the plate control and Robust Z normalized to identify the major grouping of the yeast mutants based on their redox status across organelle and nutrient conditions.

NOTE: I am also including the plots for Robust Z normalized simply to highlight that for this analysis, using Robust Z normalized is NOT appropriate.

We distinctly see from plate control normalized data that the redox status is different between the organelles (higher in mitochondria compared to cytoplasm) and within the organelles the mutants group by the nutrient conditions.

getMDSdata = function(dat) {
    mds = cmdscale(dist(t(dat)), eig = TRUE, k = 2)$points
    colnames(mds) = c("MDS1", "MDS2")
    
    col_anno = do.call("rbind", strsplit(rownames(mds), "_"))
    col_anno = col_anno[, -c(1:3)]
    colnames(col_anno) = c("Compartment", "Nutrient")
    mds = data.frame(mds, col_anno)
}

mdsZ = getMDSdata(dat = normDat.Znorm$redox_replicates)
mdsC = getMDSdata(dat = normDat.ctrNorm$redox_replicates)

p1 = ggplot(mdsZ, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Robust Z normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#1B9E77", 
    "#D95F02", "#7570B3"))

p2 = ggplot(mdsC, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Plate control normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#1B9E77", 
    "#D95F02", "#7570B3"))

pA = p1 + p2 + plot_layout(guides = "collect")

p3 <- ggviolin(normDat.Znorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#E7298A", "#66A61E"))

p4 <- ggviolin(normDat.ctrNorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#E7298A", "#66A61E"))

pB = p3 + p4 + plot_layout(guides = "collect")

p5 = ggviolin(normDat.Znorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 22, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#D95F02", 
    "#1B9E77", "#7570B3")) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

p6 = ggviolin(normDat.ctrNorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 5, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#D95F02", 
    "#1B9E77", "#7570B3")) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

pC = p5 + p6 + plot_layout(guides = "collect")

p = pA/pB/pC

ggsave(filename = paste0(path, "analysis/normalization/roGFP2_ratio_comparison_nutrient_compartments.pdf"), 
    plot = p, width = 7, height = 7)

p

Replicate similarity - Correlation

Below we show the correlation among replicates with plate control based normalization.

Distribution of normalized data

  • For per plate normalization based on plate specific control and an interactive data table to access the data

  • For per plate normalization based on median organelle specific values and an interactive data table to access the data

Session information

R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] RColorBrewer_1.1-2 pheatmap_1.0.12    patchwork_1.0.0    ggpubr_0.2.4      
 [5] magrittr_1.5       ggrepel_0.8.1      WriteXLS_5.0.0     data.table_1.12.8 
 [9] forcats_0.4.0      stringr_1.4.0      dplyr_0.8.4        purrr_0.3.3       
[13] readr_1.3.1        tidyr_1.0.2        tibble_2.1.3       ggplot2_3.2.1     
[17] tidyverse_1.3.0    DT_0.12            rmdformats_0.3.6   knitr_1.28        

loaded via a namespace (and not attached):
 [1] httr_1.4.1        jsonlite_1.6.1    modelr_0.1.5      shiny_1.4.0      
 [5] assertthat_0.2.1  cellranger_1.1.0  yaml_2.2.1        pillar_1.4.3     
 [9] backports_1.1.5   lattice_0.20-38   glue_1.3.1        digest_0.6.23    
[13] promises_1.1.0    ggsignif_0.6.0    rvest_0.3.5       colorspace_1.4-1 
[17] htmltools_0.4.0   httpuv_1.5.5      plyr_1.8.5        pkgconfig_2.0.3  
[21] broom_0.5.4       haven_2.2.0       bookdown_0.17     xtable_1.8-4     
[25] scales_1.1.0      later_1.0.0       generics_0.0.2    farver_2.0.3     
[29] ellipsis_0.3.0    withr_2.1.2       lazyeval_0.2.2    cli_2.0.1        
[33] mime_0.9          crayon_1.3.4      readxl_1.3.1      evaluate_0.14    
[37] fs_1.3.1          fansi_0.4.1       nlme_3.1-144      xml2_1.2.2       
[41] tools_3.6.2       hms_0.5.3         formatR_1.7       lifecycle_0.1.0  
[45] munsell_0.5.0     reprex_0.3.0      compiler_3.6.2    rlang_0.4.4      
[49] grid_3.6.2        rstudioapi_0.11   htmlwidgets_1.5.1 crosstalk_1.0.0  
[53] labeling_0.3      rmarkdown_2.1     gtable_0.3.0      DBI_1.1.0        
[57] reshape2_1.4.3    R6_2.4.1          lubridate_1.7.4   fastmap_1.0.1    
[61] stringi_1.4.5     Rcpp_1.0.3        vctrs_0.2.2       dbplyr_1.4.2     
[65] tidyselect_1.0.0  xfun_0.12

Ashwini Kumar Sharma, PhD

2021-06-18